A Note on Young's Raising Operator
Glânffrwd P. Thomas · Canadian Journal of Mathematics · 1981
Consider the following formula due to Young [ 7 ] for the calculation of the homogeneous product sum, h λ , in terms of Schur functions; where the operation S rs is defined as follows: Y 1 : S rs , where r < s , “represents the operation of moving one letter from the s -th row up to the r -th row; and the resulting term is regarded as zero, when any row becomes less than a row below it, or when letters from the same row overlap; as, for instance, happens when λ 1 = λ 2 in the case of S 13 S 23 .“ The following example of the above is given by Robinson [ 4 ]. Calculation by other means shows that the above analysis of h (3,2,1) is correct; however, it will be noticed that the operator S 12 3 S 23 does not appear in the above yet it is not specifically excluded by the rule Y 1 .